Rewrite as a simplified fraction. ${0.2\overline{3} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 23.3333...\\ 10x &= 2.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 21}$ ${x = \dfrac{21}{90}} $ ${x = \dfrac{7}{30}} $